Dynamics Analysis Of Material Cycle In A Class Of Ecosystems

Phosphorus is one of the main nutrient elements needed by plants,which plays a key role in plant growth and also affects the overall stability of the pond ecosystem.Therefore,it is of great significance to quantitatively analyze the internal mechanism of phosphorus cycle in the pond ecosystem and scientifically regulate the phosphorus cycle in the pond ecosystem.Firstly,according to the characteristics of phosphorus cycle and the characteristics of reservoir circulation in pond ecosystem and the theory of infectious disease model,the dynamic equation of phosphorus cycle is established.The positive equilibrium points and thresholds of the modles are obtained,and the controllable factors and ranges affecting the phosphorus cycle as well as the characteristic conditions for maintaining the steady state of the phosphorus cycle were analyzed.The asymptotic stability of the equilibrium point is proved by Hurwitz theorem.The results of theoretical analysis are verified by simulation.Secondly,considering that the number of fish in ponds that consumers mainly breed is limited by environmental factors.the number of consumers will have an environmental capacity that shows an exponential growth in the form of logistic.On the basis of the original model,the phenomenon of consumer saturation in ponds is represented by bounded function called g(c)=c/(1+ac).A phosphorus cycle model with consumer saturation is established and the data are simulated.Finally,the delay phenomenon of phosphorus release from sediments in ponds is considered.A kinetic model of phosphorus cycle with time delay is established by combining the epidemic model with the theory of time delay.The dynamic equation of phosphorus cycle with time delay is listed.The positive equilibrium point of the equation is obtained.The stability of the delay model is analyzed and Hopf bifurcation is calculated.By adjusting the controllable factors of phosphorus cycle,the simulation analysis was carried out.